A firm produces output according to a production function: Q = F ( K,L ) = min {

Question

A firm produces output according to a production function:

Q = F(K,L) = min {3K,3L}.

a. How much output is produced when K = 2 and L = 3?




b. If the wage rate is $40 per hour and the rental rate on capital is $25 per hour, what is the cost-minimizing input mix for producing 6 units of output?

Capital:
Labor:


c. How does your answer to part b change if the wage rate decreases to $25 per hour but the rental rate on capital remains at $25 per hour?

Capital increases and labor decreases. Capital and labor increase. Capital decreases and labor increases. It does not change.

Explanation / Answer

a) We are given Q = F(K,L) = min {3K,3L}

So if K = 2 and L =3 we have
min {3(2),3(3)} thus

min {6,9} and Q = 6

b) To produce Q =6 we need to buy at least 2 units of K and L so min (3K,3L) gives 6 . If the wage rate is $40 per hour and the rental rate on capital is $25 per hour, then the cost-minimizing input mix for producing 6 units of output will be 2 units of K and 2 units of L

C) It does not change as it is min function where good are used in fixed proportion.

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